Sum matrix elements group by indices in Python

I have two matrix (same row and column): one with float values, which are grouped by indices in the other matrix. As a result, I want a dictionary or a list with the sums of the elements for each index. Indices always start at 0.

A = np.array([[0.52,0.25,-0.45,0.13],[-0.14,-0.41,0.31,-0.41]])
B = np.array([[1,3,1,2],[3,0,2,2]])

RESULT = {0: -0.41, 1: 0.07, 2: 0.03, 3: 0.11}

I found this solution, but I'm searching for a faster one. I'm working with matrix with 784 x 300 cells and this algorithm takes ~28ms to complete.

import numpy as np

def matrix_sum_by_indices(indices,matrix):
    a = np.hstack(indices)
    b = np.hstack(matrix)
    sidx = a.argsort()
    split_idx = np.flatnonzero(np.diff(a[sidx])>0)+1
    out = np.split(b[sidx], split_idx)
    return [sum(x) for x in out]

If you can help me find a better and plain solution to this problem, I'll be grateful!

EDIT: I made a mistake, time to complete is ~8ms in a 300*10 matrix, but ~28ms in a 784x300.

EDIT2: My A elements are float64, so bincount give me ValueError.

3 answers

  • answered 2018-07-10 15:16 Eelco Hoogendoorn

    The numpy_indexed package has efficient and simple solutions to this problem (disclaimer: I am its author):

    import numpy_indexed as npi
    keys, values = npi.group_by(B.flatten()).sum(A.flatten())

  • answered 2018-07-10 15:16 user3483203

    You can make use of bincount here:

    a = np.array([[0.52,0.25,-0.45,0.13],[-0.14,-0.41,0.31,-0.41]])
    b = np.array([[1,3,1,2],[3,0,2,2]])
    N = b.max() + 1
    id = b + (N*np.arange(b.shape[0]))[:, None] # since you can't apply bincount to a 2D array
    np.sum(np.bincount(id.ravel(), a.ravel()).reshape(a.shape[0], -1), axis=0)


    array([-0.41,  0.07,  0.03,  0.11])

    As a function:

    def using_bincount(indices, matrx):
        N = indices.max() + 1
        id = indices + (N*np.arange(indices.shape[0]))[:, None] # since you can't apply bincount to a 2D array
        return np.sum(np.bincount(id.ravel(), matrx.ravel()).reshape(matrx.shape[0], -1), axis=0)

    Timings on this sample:

    In [5]: %timeit using_bincount(b, a)
    31.1 µs ± 1.74 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
    In [6]: %timeit matrix_sum_by_indices(b, a)
    61.3 µs ± 2.62 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
    In [88]: %timeit scipy.ndimage.sum(a, b, index=[0,1,2,3])
    54 µs ± 218 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)

    (scipy.ndimage.sum should be faster on much larger samples)

  • answered 2018-07-10 15:40 Thomas Baruchel

    The following solution, relying on scipy.ndimage.sum is highly optimized for speed:

    import numpy as np
    A = np.array([[0.52,0.25,-0.45,0.13], [-0.14,-0.41,0.31,-0.41]])
    B = np.array([[1,3,1,2], [3,0,2,2]])
    import scipy.ndimage
    print(scipy.ndimage.sum(A, B, index=[0,1,2,3]))

    You may have to work a little for having the index parameter be exactly what you want. It is the list of the indices you want to get in the result. Maybe the following will be a good starting point:

    print(scipy.ndimage.sum(A,B, index=np.unique(B)))

    but if you know by advance the list of all indices, it will be more efficient to hard-code it here.